Acoustic wave filter



May 23, 1933- R. a BOURNE 1,910,672

ACOUSTIC WAVE FILTER Filed May 13, 1932 2 Sheets-Sheet 2 0' I00 Fug. e00 .900

10o Fwy. 000 00 400 IN VEN TOR BY Rom/v12 5500mm A TTORNEYS Patented May 23, 1933 lJNITED STATES PATENT OFFICE ROLAND B. BOU'RNE, OF HARTFORD, CONNECTICUT, ASSIGNOR TO THE MAXIM SILENCER COMPANY, OF HARTFORD, CONNECTICUT, A CORPORATION OF CON- NECTICUT ACOUSTIC WAVE FILTER Application filed May 13, 1932. Serial No. 611,060.

The present invention relates to devices of the wave filter type, particularly to those structures wherein the acoustic properties of mass and elasticity are uniformly distributed; that is, to structures having physical dimensions such that wave motion or change of phase takes place within the various discreet parts thereof. An example of an acoustic structure having uniformly distributed constants of mass and elasticity is the organ pipe.

The advantages of employing structures of the Wave filter-type for attenuating certain sound frequencies known to exist in the exhaust conduits of internal combustion engines, and the like, are evident when it is considered that straight, smooth, unobstructed conduits may be employed for 1 in time become 'ation band, which in the passage of the exhaust gases, that hi h degrees of attenuation are obtainable, that wide bands of sound frequencies may be made to suffer attenuation, that the physical construction may be made extremely simple and cheap to manufacture and that no small holes, fine interstices or complicated baflles and passageways which might clogged with carbon, etc. are necessary.

The prior art teaches how to construct certain acoustic wave filters. In the past, stress has been laid on structures having a series of relatively narrow attenuation bands with correspondingly wide passbands and upon structures having but a single attenupractice turns out to be none too wide, Where the main object is to offer attenuation, especially over a wide frequency range.

The main object of this invention is to provide an acoustic wave filter having, in its attenuation vs. frequency characteristic, a series of wide attenuation bands separated by extremely narrow passbands.

Another object of the invention is to provide an acoustic wave filter having a series of harmonically related, narrow passbands.

A further object of the invention is to provide a stricture, having predictable acoustic attenuation characteristics, said structure being extremely simple to design and fabricate on a commercial scale.

To assist in a more complete understanding of the invention, reference is now made to the drawings wherein- Fig. 1 shows a generalized recurrent ladder-type structure involving both series and shunt impedances;

Figs. 2, 3, and 4 show various embodiments of acoustic wave filters;

Figs. 5, 6, 7, and 8 show the attenuationfrequency characteristics of various embodiments of the invention.

For the purposes of this invention, structures having distributed impedance constants of mass and elasticity are constructed of tubes or conduits which are an appreciable fraction, or greater, of a wavelength long and in which, therefore, wave motion or progressive change of base takes place along the length thereof Structures in which no appreciable wave motion or changeof phase, as a function of length, takes place, are considered as having lumped impedance constants of mass and elasticity and may be represented by a closed volume together with a communicating orifice or neck, short in comparison to a wavelength.

Since the invention embodies structures employing both kinds of impedance elements as sidebranches, it is desirable to give a fundamental equation which will represent the attenuation-frequency characteristic of all the embodiments shown. For structures employing tubular main line or series conduits of uniform cross-sectional area, it can be shown that L we coshP-cos 0 It will be seen that cosh P is, in general, a complex quantity, having both real and imaginary components. Since, in the structurcs embodying this invention, acoustic resistance maybe kept to a low value, it is per missihle to neglect the etl'ects of acoustic resistance and frictional dissipation and to consider the impedance elements as pure rcactances. From this it follows that the propagation constant I is either a real quan tity or else an imaginar one. Since cosh 1 cannot be less than plus one nor greater than minus one, it follows that l is real for all values of cosh P lying outside the above limits, in which case 1 represents the attenuation per section of the structure in nepers. To convert ncpers to the more common decibel unit of attenuation it is only necessary to multiply the result by 8.686. \Vhen the value of the right-hand side of Equation (1) falls between plus one and minus one, it represents the phase change per section of the filter, the attenuation constant, ffll' tlicst values, being zero. Such values indicate a passband and the cut-off frequen cies occur when cosh P equals plus or minus one.

Considering Equation (1), it isv evident that if appropriate values for Z, and Z are chosen and substituted therein, the equation governing specific structures embodying the foregoing principles will at once be obtained. In all the cases pertinent to this invention, the value of Z is taken equal to where p is the density of the medium and S the cross-sectional area of the main conduit. This is obtainable directly from the fundamental equation showing the velocity of sound in a gaseous medium. This quantity is in the nature of a resistance since it does not involve a consideration of frequenov. The value of Z will depend upon the nature of the shunt branch used. Since the invention is largely concerned with exhaust discharges from internal combustion engines and the like, itis evident that sidebrauches open to the atmosphere cannotbe used and the choice of sidebranches to give desired etl'ects rests among those sidebranches which are closed.

The simplestsidebranch meeting this requi'rement is a tubular member coupled to the main channel and closed at its remote end. Such a tube is a quarter of a wavelength long for the fumlamental resonant frequency. It is also resonant. at odd harmonics of the fundamental frequency. Placed in shunt to an infinitely long conduit, it offers zero impedance, looking into it from the main conduit, to its resonant frequencies and relatively high but diminishing attenuation to adjacent frequencies.

I The width or broadness of the band depends upon the relative areas of the sidebranch and main conduit, being broader as the area. of the sidebranch is increased with respect to that of the main conduit. \Vhen now a plurality of similar closed sidebranches are connected in shunt to the main conduit at equal intervals along its length, the series and shunt impedance functions conspire to give not only attenuation bands, but also pass bands, wherein negligible attenuation occurs. In this kind of a structure, the sections of the main conduit are of equal length and are terminated in the same manner; consequently, they may for convenience be considered to behave as if resonant to those frcqnencies for which the distance between successive sidebranchcs is one-half length and all the harmonics thereof, both even and odd. If now, the lengths of the sidebranches and distance between them be so chosen that resonance occurs in both for the same frequency, the impedance functions conspire to limit the amount of attenuation at resonance to a finite value and to broaden the band of frequencies over which attenuation occurs. Since a filter structure having inherently narrow attenuation bands is commercially impracticable, however great the attenuation therein may be, due to unknown variations in the velocity of sound in the medium (hot exhaust gas, in many cases), commercial requirements dictate the use of structures otfering the widest possible attenuation bands.

As pointed out above, the value of Z,, the

impedance of the main channel, is given by the relatlon aQ Z1- 8, A corresponding relation fora sidebranch Considering now a filter wherein the shunt branches are closed tubes of equal length coupled to the main conduit at intervals along the length thereof equal to twice the length of the sidebranch tubes, Equation (4) becomes tan (5) The construction of A consideration of the sine and; tangent functions, above, shows that whenever the tangent is infinity the sine is zero; and further, since the sine is changing twice as fast as the tangent, an alternate series of values makes both the sine and tangent zero simultaneously. This gives rise to an harmonically related series of broad attenuation bands which are, however, separated by pass bands of substantially the same width. Since an important object of the invention is to provide attenuation over as wide a range of frequencies as possible, it is necessary, in order to secure a commercially practicable device, to fill in as many of these undesirable passbands as possible, with attenuation bands. This'may be accomplished mathematically by adding another tangent function to the Equation said function changing one-quarter as fast as the sine function; physically, this is accomplished by adding another closed tubular sidebranch in parallel at each junction point along the length of the conduit, the additional sidebranches being one-quarter as long as the distance between sidebranches along the main channel.

By making the proper substitution in Equation (5) it is evident that i (0L1 (0L1 (0L1 cosh cos sm [tan This equation holds'for the condition that the areas of both paralleled sidebranches are equal.

A plot of this equation is shown in Fig. 5, the large portion of the'frequency spectrum consumed by attenuation bands being evident. The commercial embodiment of the invention operating under Equation (6) is shown in Fig. 2. In this embodiment, the filter is of two sections, the minimum permissible under the theory. The area of the sidebranch conduits are equal and may be made much larger than the area of the main conduit, due to the concentric construction. this device is so simple as .to be self-evident from the figure, involving as it does two concentric tubular members 10 and 11 and three headers 12, 13, and 14 positioned as shown. The openings 15 in the main conduit, giving in to the annular side conduits are not'critical in design, it being only necessary to make the length of the slot-like opening of the order of the diameter of the main channel.

Considering further the plot shown in Fig. 5, the ordinates are plotted in decibels for two sections. The passbands, while of two' different sets of widths, occur in sub- .the attenuation bands.

stantially harmonic relation to each other and at values of where n is any integer or zero One method of using the several broad attenuation bands obtained is to arbitrarily place the seventh harmonic of the fundamental frequency to be attenuated at This procedure place the first six harmonics of the fundamental frequency well within Commercially speaking, harmonics above the sixth are of little importance, although it may be pointed out that with the exception of the seventh, the first thirteen harmonics all fall inside attenuation bands.

It is now apparent that, in order to de sign a filter of this type to attenuate greatly a sound wave of known frequency and having considerable harmonic content, it is only necessary, once the cross-sectional area of the main conduit is fixed, to substitute the proper values in the equation and solve for the value of L, the other dimensions being apparent by inspection.

A. further important use of the filter is as a bandpass filter, where it is desired to permit transmission of a very narrow band of frequencies and all their harmonics. Select mg a value of high frequency sounds is .greatly removed from the realm of those devices which depend upon acoustlc resistance for attenuation, thus permitting much more eflieient and economical constructions.

Another example of two unlike 1mpedances in parallel .a side branch is shown in Fig. 3. Here, the main channel of length L and area S has coupled to it the lumped impedances represented by the volumes V and V together with the coupling orifices or conductivities C and C 2, respectively. By substituting the proper values for a structure of this kind in Equation (1), there results V A plot of Equation (8) is shown in Fig. 6, attenuation being plotted against frequency in this case. A unique feature of this filter is found in the fact that the (llS-I tance between sidcbranch junction points along the main channel is one-half Wave length for the resonant frequency of the larger of the two paralleled sidebranches and a full wave length for the smaller of the two. The broadening effect of the correlation described above between the spacing of the junction points along the main channel and the resonant frequene of the sidebranehes is again noted. Tfie plot of Equation (8) is not carried beyond the upper cutoff frequency of the second attenuation band, since with the construction shown in Fig. 3, the exact behavior of the sidebranches for the higher frequencies is not readily determined mathematically.

Fig. 4 show-s an acoustic wave filter in which the main channel has coupled to it the unlike parallel impedances represented respectively by the linear sidebranch L282 and the volumetric sidebranch G V. The equation for a filter of this type is A plot of this eguation is shown in Fig. 7 This particular lter has the frequencies of maximum attenuation placed at 100 cycles and 150 cycles for the linear and volumetric sidebranches respectively. The distance between junction points along the main channel is. in the. particular case chosen for illustration, a half wave length for 100 cycles but not for 150 cycles. The first three attenuation bands only are plotted, the resulting shapes being clearly shown. Another variation of this type filter is obtained by placing the fl'indamental frequenc of the volumetric system at twice the fundamental frequency of the tubular sidebranch. The normally infinite attenuation at particular frequencies due to a sidebranch. is reduced to a finite quantity, and atthe same time the attenuation bands are widened, by spacing the junction points along the main channel equal to a multiple of a half wave length of the frequency for which the sidebranch is resonant. Fig. 7 shows this clearly for the attenuation bands due to the tubular sidebranch. In Fig. 8 this effect is extended to the volumetric sidebranch. The plot, shown in Fig. 8 is similar to that shown in Fi 5 for the first three attenuation bands, adthoug'h the passbands may not necessarily be harmonic, depending upon the design of the volumetric sidebranch. The effect of increasing the conductivity of the volumetric sidebranch, for a given frequency, is to broaden the attenuation band, thus displacing slightl the adjoining bands.

It is obvious that tiiree or more parallel sidebranches might be used, giving various characteristics. In general, it may be stated that increasing the number of paralleled sidebranches results in increasing the number of pass and, therefore, attenuation bands.

The choice of a particular filter resolves into 7 a knowledge of the conditions to be met.

In all acoustic wave filters, the theory assumes either an infinite number of sections or a finite number terminated in a structure having an impedance-equal to the characteristic impedance of the filter. In practice, this is not altogether realizable, but a sufficient approximation for commercially satisfactory results ma be obtained by the use of straight conduits of proper length.

I claim:

1. An acoustic wave filter comprising a main sound conduit of uniform cross-sectional area, said conduit having, at equally spaced intervals along the length thereof, a plurality of equal acoustic impedances disposed in shunt with and acoustically coupled to said main conduit, said acoustic impedances each comprising two or more unlike closed acoustic sidebranches in parallel.

2. An acoustic wave filter in accordance with claim 1 in which the sidebranch impedances comprise two or more closed tubes of uniform cross-sectional area and of-unequal length, ,in parallel.

3. An acoustic wave filter in accordance with claim 1 in which the sidebranch impedanccs comprise two closed tubes of uniform cross-sectional area in parallel, one of which is half as long as the distance between sidebranches along the main conduit and the other of which is one-quarter of said distance.

4. An acoustic wave filter in accordance with claim 1, in which the sidebranch impedances comprise two closed chambers of different volume, in parallel, communicating with said main sound conduit through orisound conduit through orifices therein, the

lumped impedance system comprising one of said volumes, together with-its communicating orifice, resonating to a frequency for 5 which the distance along said main sound conduit between said sidebranch impedances is one-half wave length, and the system comprising the other of said volumes, together with its communicating orifice, resonating to twice that frequency.

(3. An acoustic wave filter in accordance with claim 1 in which the sidebranch impedances comprise,respectively, a uniform tubular conduit, closed at its remote end, in parallel with a closed chamber coupled to said main sound conduit through orifices. 7. An acoustic wave filter in accordance with claim 1 in which the sidebranch impedanccs comprise, respectively, a uniform tubular conduit, closed at'its remote end, in parallel with a closed chamber coupled to said main sound conduit, through orifices, wh -eby the lumped acoustic system comprising said chamber and orifices resonates to a frequency equal to twice the fundamental frequency of said tubular member.

8. An acoustic wave filter comprising a uniform, tubular, main sound conducting (hannel having two openings therein in spaced relation along the length ofv said channel, each of said openings communicating with a uniform, tubular, laterally disposed conduit, closed at both ends, at a point distant from one end thereof equal to onethird its total length.

9. An acoustic wave filter comprising two concentric uniform tubular members radially spaced one from the other, end closures extending between the members, and an in- 9 termediate partition also extending therebe tween, whereby are formed a central tubular conduit and two equal annular chambers surrounding it, said annular chambers being long in proportion to the wavelengths to be 0 attenuated so that appreciable acoustic wave motion takes place therein, and openings from the central conduit into the annular chambers in spaced relation along the length of the central conduit and asymmetri- 0 cally located with respect to the length of each annular chamber whereby the central conduit is acoustically coupled to the two annular chambers.

10. An acoustic wave filter comprisiing 5 two eccentric uniform tubular members radially spaced one from the other, end closures extending between said members, and an intermediate partition also extending therebetween, whereby are formed a central tubular conduit and two equal annular chambers surrounding it, said annular chambers being long in proportion to the wave lengths to be attenuated 'so that appreciable acoustic wave motion takes place therein, and openings from the central conduit into the annular chambers at points one-third the distance from each end closure to the intermediate partition whereby the central conduit is acoustically coupled to the two annular conduits.

11. An acoustic wave filter comprising a main conducting channel, openings therein in spaced relation along the length thereof, and a pair of closed, annular, tubular sidebranches of unequal length communicating in parallel with each of said openings. 12. An acoustic Wave filter comprising a main conduct-ing channel, openings therein in'spaced relation along the length thereof, and a pair of closed, annular, tubular sidebranches of unequal length communicating in parallel with each of said openings, one of each pair of sidebranches being twice as long as the other of the pair.

13. An acoustic wave filter comprising a main conducting channel, openings therein in spaced relation along the length thereof, and a pair of closed, annular, tubular sidebranches of unequal length communicating in parallel with each of said openings, the cross-sectional area of said sidebranches being large compared to that of the main con ducting channel.

14. An acoustic wave filter comprising a central conduit having circumferential slots spaced along its length, an external casing, headers closing the space between the conduit and the casing atthe ends of the casing, a partition joining the conduit and the easing intermediate the slots, and annular partitions extending from the casing towards the conduit with their free edges in adjacency with the slots.

15. An acoustic wave filter comprising a central conduit, an external casing, headers closing the space between the conduit and the casing at the ends of the casing, a partition joining the conduit and the casing at the longitudinal midpoint of the casing, the conduit being formed with circumferential slots located one-third of-the distance between each header and the central partition, and annular partitions extending from the casing towards the conduit with their free edges in adjacency with the slots.

16. An acoustic wave filter comprising a main acoustic conduit having acoustic junctions spaced along its length, and a plurality of closed acoustic sidebranches arranged in groups at each of the several acoustic junctions, the sidebranches forming the group at each junction having different fundamental resonant frequencies related one to another in the ratio of small integers and having a common acoustic coupling to the main acoustic conduit at said junction.

17. An acoustic wave filter comprising a main acoustic conduit having acoustic junctions spaced along its length, and a plurality of closed acoustic sidebranches arranged in groups at each of the several acoustic junctions, the sidebranches forming the group at each junction having different flmdamental resonant frequencies related one to another as integral multiples and having a common acoustic coupling to the main acoustic eonduit at said junction.

18. An acoustic wave lilter comprising a main acoustic conduit having acoustic junc- 10 tions spaced along its length at. intervals equal to the wave length of one frequency to be attenuated, and a plurality of closed acoustic sidebranches arranged in groups at each of the several acoustic junctions. the

sidehranches forming the group at each junction having different fundamental resonant.- frequencies of which one correspoluls to said frequency to be attenuated and another is an integral multiple thereof, and having a common acoustic coupling to the main acoustic conduit at said junction.

19. An acoustic wave filter comprising a main sound conduit of uniform cross-sectional area, and a plurality of equal acoustic impedances disposed in shunt with and acoustically coupled to the main conduit at intervals along its length equal to twosevenths the velocity of sound in the medium divided by the major frequency to be. at-

tenuated, each of said impedances comprising a pair of closed tubes of uniform crosssectional area, one of which is half as long as the interval between the side branches and the other is one-quarter of that interval.

In testimony whereof I have atlixed my signature.

ROLAND B. BOURNE.

CERTIFICATE OF CORRECTION.

Patent No. 1,910,672. May 23, 1933.

ROLAND B. BOURNE.

It is hereby certified that error appears in the printed specification of the above numbered patent requiring correction as iollowsz Page 3. line 79, for "place" read "places"; page 5, line 55. claim 10, for "eccentric" read "concentric"; and that the said Letters Patent should be read with these corrections therein that the same may conform to the record of the case in the Patent Office.

Signed and sealed this 25th day of July, A. D. 1933.

M. J. Moore (Seal) Acting Connniasioner of Patents. 

